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Unformatted text preview: 1 Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows 2 Chapter 5 Learning Goals LG1: Compound multiple cash flows to the future LG2: Compute the future value of frequent, level cash flows LG3: Discount multiple cash flows to the present LG4: Compute the present value of an annuity LG5: Find the present value of a perpetuity LG6: Recognize and adjust values for beginning-of-period annuity payments as opposed to end-of-period annuity payments LG7: Explain the impact of compounding frequency and the difference between the annual percentage rate and the effective annual rate LG8: Compute the interest rate of annuity payments LG9: Compute payments and amortization schedules for car and mortgage loans LG10: Calculate the number of payments on a loan 3 Introduction The previous chapter involved moving a single cash flow from one point in time to another Many business situations involve multiple cash flows Annuity problems deal with regular, evenly-spaced cash flows Car loans and home mortgage loans Saving for retirement Companies paying interest on debt Companies paying dividends 4 Consider the following cash flows: you make a $100 deposit today, followed by a $125 deposit next year and a $150 deposit at the end of the second year. If interest rates are 7%, what is the future value of your account at the end of the 3 rd year? 1 2-100-125-150 ... 3 5 Notice that the first deposit will compound for 3 years, the second deposit will compound for 2 years, and the last deposit will compound for 1 year. We can calculate the future value of each deposit individually and add them up to get the total FV 3 = $122.50 + $143.11 + $160.50 = $426.11 1 2-100-125-150 ... 3 Example 5.1: Saving for a car Say that as a freshman in college, you will be working as a house painter in each of the next three summers. You intend to set aside some money from each summers paycheck to buy a car for your senior year. If you can deposit $ 2,000 from the fi rst summer, $ 2,500 in the second summer, and $ 3,000 in the last summer, how much money will you have to buy a car if interest rates are 5 percent? SOLUTION: The first cash flow, which occurs at the end of the first year, will compound for two years. The second cash flow will be invested for only one year. The last contribution will not have any time to grow before the purchase of the car. Using equation 5- 1, the solution is FV3= 2,000*(1+0.05)^2 + 2,500*(1+0.05)^1 + 3,000*(1+0.05)^0 =2 000*1.1025 + 2500*1.05+ 3000*1= $7,830 You will have $ 7,830 in cash to purchase a car for your senior year. View interactive Example 5.1 (move the cursor to the highlight area, right click your mouse and click Open Hyperlink) You can view interactive examples in other formats at http://highered.mcgraw-hill.com/sites/0073382256/student_view0/chapter5/interactive_exam 7 Now, suppose that the cash flows are the same each period Level cash flows are common in finance. These problems are known as annuities FVA N = PMT( ) (1+i) ^N- 1 i 8...
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